Flow Characteristics of Curved Rotor Stator Systems Using Large Eddy Simulation

  • Mohammad Darvish Damavandi
  • Amir NejatEmail author


In this paper, the new idea of application of a curved rotor disk in rotor stator systems is presented and analyzed by using the large eddy simulation technique. The geometry of the examined rotor-stator system consists of a stationary flat disk (stator), a rotating curved disk (rotor) and a stationary enclosing cylinder (shroud). A hole in the center of stator allows the flow to enter the cavity, and the clearance between the shroud and rotor enables the flow to exit the cavity. Employing elliptical bumps with different geometrical parameters on the rotor disk (creating a curvature on the rotor), the rotating curved disk is parametrized. Three cavity cases (one with a flat rotor disk, another with the maximum outflow total pressure, and the third with the highest mass flow rate) are selected for LES analysis and more detailed investigation of flow and turbulence structures. The Favre-filtered governing equations for LES analysis of compressible turbulent flows are solved for all three cases. Radial and circumferential flow velocities as well as shear and normal Reynolds stresses in different cavity regions are studied. The flow in a rotor-stator cavity is simultaneously affected by the inlet flow, rotor rotation, and the bump on rotor disk. Creating a bump on rotor disk causes increase of both the radial pressure gradient and the mass flow rate of fluid that enters the rotor-stator cavity.


Curved rotor disk Elliptical bump LES Reynolds stresses Outflow total pressure Boundary layer 



Semi-minor axis of elliptical bump (m)


Semi-major axis of elliptical bump (m)


Non-dimensional mass flow rate


Total energy (J)


Gap ratio


Shroud clearance ratio


Distance between the center of elliptical bump and rotation axis (m)


Entrainment coefficient


Inlet radius (m)


Moment applied on rotor (N m)


Mach number

\( \dot{m} \)

Mass flow rate (kg s−1)


Total pressure difference between inlet and outlet (bar)


Static pressure (bar)


Prandtl number


Heat flux vector (W m−2)


Disk radius (m)


Rotational Reynolds number


Reynolds stress tensor with i, j = (r,θ, z)

r, θ, z

Cylindrical coordinate


Distance between disks (m)


Clearance between rotor and shroud (m)

\( {\overset{\sim }{S}}_{ij} \)

Resolved strain rate tensor


Total temperature (K)


Static temperature (K)


Time (s)


Cartesian velocity components (m s−1)

Vr, Vθ, Vz

Radial, circumferential and axial velocity components (m s−1)

\( {v}_r^{\prime },{v}_{\theta}^{\prime },{v}_z^{\prime } \)

Fluctuation of radial, circumferential and axial velocity components (m s−1)

xi i-th

Cartesian coordinates (m)



Direct numerical simulation


Finite difference


Implicit large eddy simulation


Large eddy simulation


Reynolds averaged Navier-Stokes


Root mean square


Spectral vanishing viscosity


Sub-grid scale

Greek Symbols


Turbulent stress on the scalar level


Sub-grid scale pressure-velocity


Specific heat ratio


Kronecker delta


Rate of dissipation


Kolomogorov length scale


Sub-grid scale turbulent dissipation rate


Turbulent flow parameter


Dynamic viscosity (N s m−2)


Kinematic viscosity (s−1 m2)


Sub-grid scale pressure-dilatation


Fluid density (kg m−3)


Viscous stress tensor


Sub-grid scale stress tensor


Rotational speed (rpm)



Basic cavity configuration (flat rotor)


Modified cavity configuration (rotor with elliptical bump)

Other Operators

\( \overline{.} \)


\( \overset{\sim }{.} \)

Favre filtering

\( \widehat{.} \)

Indicates that the quantity is based on filtered variables

\( \overset{=}{.} \)

Shows the unit surface normal



The result of this article is a part of ongoing PhD research thesis and there was no funding for this research.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mechanical Engineering, College of EngineeringUniversity of TehranTehranIran

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